Skip to content
Studycaller

CA Foundation doubt

If 3^a = 5^b = 75^c, what is the value of ab - c(2a + b)?

Ch ratio , proportion , indices and logarithm. Question 34 which i posted

Ch ratio , proportion , indices and logarithm. Question 34 which i posted

Image attached to the doubt: Ch ratio , proportion , indices and logarithm. Question 34 which i posted

Asked by Sunidhi··1 answer

1 reply

  1. BrunoAI answerAI first answer — verify with your teacher

    Answer: (b) 0 Let 3^a = 5^b = 75^c = k. 1. Then 3 = k^(1/a), 5 = k^(1/b), 75 = k^(1/c). 2. Since 75 = 3 x 5 x 5, we get k^(1/c) = k^(1/a) x k^(2/b). 3. Equate the powers: 1/c = 1/a + 2/b = (b + 2a)/ab. 4. So ab = c(2a + b), which gives ab - c(2a + b) = 0. Tip: Q33, Q35 and Q36 use the same trick. Put everything equal to k and break the last base into prime factors.

Related questions

What is the shortcut for questions like 2^x = 3^y = 6^z?

Put each expression equal to k and use 6 = 2 x 3, which gives 1/z = 1/x + 1/y.

Which law of indices is used in these questions?

The product law, a^m x a^n = a^(m+n), is used to equate exponents once all bases are written as powers of the same k.

Can logarithms be used instead?

Yes, taking logs of each expression gives a log 3 = b log 5 = c log 75, which leads to the same relation.

Have a doubt like this, or know the answer?

Ask and reply in the free Studycaller app. Students and Bruno answer fast.

Add your own doubtReply to this doubt
Get a CA mentor

Related doubts

  • CA FoundationSale of Goods Act 1930 - sale on approval or return

    How should my answer on goods sent on approval and later pledged by the buyer be evaluated and marked?

    BrunoAI answer

    Your conclusion is correct, but the main reasoning is off. Estimated score: about 2 to 2.5 out of 4. Marks (a typical 4-mark split): - Provision of Section 24: 1/2. You quoted only the time-lapse rule. - Application to facts: 0.5/1. Wrong ground used. - Conclusion and recourse: 1/1. What cost you marks: 1. The key rule is Section 24(a). Property passes when the buyer signifies approval or does any act adopting the transaction. Joshi's pledge is that act, so property passed to him at the time of the pledge, not because a "reasonable time" lapsed. 2. Section 29 (seller under a voidable contract) does not apply here. Section 30(2) is not needed either. Drop both. 3. Small slips: Ganesh is a "he", and "bought" not "brought". Ganesh is a pledgee, not a buyer. Ideal line: "Pledging is an act adopting the transaction, so property passed to Joshi and Ganesh gets a good title. Preeti cannot recover the car and can only claim the price from Joshi."

    Read full answer →

    1 answer 15 Nov 2026

  • CA FoundationAS 3 Cash Flow Statement - interest and dividend classification

    Why are cash flows of a financial entity treated differently from those of a non-financial entity?

    Veer

    Dono ke cash flow treatment me farq isliye hai kyunki dono ka main business (core operation) alag hota hai. • Non-Financial Entity: Inka main kaam goods/services bechna hai, isliye loan aur interest inke liye Investing/Financing hai. • Financial Entity (Banks): Inka main kaam hi paisa lena-dena hai, isliye interest aur loans inke liye Operating hai.

    Read full answer →

    2 answers 15 Nov 2026

See all CA Foundation doubts

Free app · 5 lakh+ learners

Ask your doubt in the Studycaller app

Read full notes, ask doubts, follow toppers and track your study hours — free on Android and iPhone.

Get it onGoogle PlayDownload on theApp Store